Here is the full list of all 50 Adventure of Leek achievements.
Lose 100 Lives
Defeat 100 skull things
Defeat 100 snails
Defeat 100 worms
Throw 1000 Water Balloons
Beat Lava Land I (Without Dying)
Look through the credits
Beat Lava Land III (Without Dying)
Beat The Game
Defeat Plum
Complete Speedrun Mode in less than 10 minutes
Beat Lava Land II (Without Dying)
Defeat 10 skull things
Defeat 10 snails
Defeat 10 worms
Attempt Speedrun Mode
Beat Lava Land III
Collect All The Coins (Lava Land III)
Beat Lava Land II
Collect All The Coins (Lava Land II)
Lose 10 lives
Throw 100 Water Balloons
Beat Lava Land I
Collect All The Coins (Lava Land I)
Beat Worm Caves III (Without Dying)
Defeat The Serpent
Enter Lava Land
Beat Worm Caves III
Collect All The Coins (Worm Caves III)
Beat Worm Caves II (Without Dying)
Beat Worm Caves II
Beat Worm Caves I (Without Dying)
Collect All The Coins (Worm Caves II)
Beat Worm Caves I
Collect All The Coins (Worm Caves I)
Beat Canyons III (Without Dying)
Defeat The Moquito Brothers
Enter The Worm Caves
Beat Canyons III
Collect All The Coins (Canyons III)
Beat Canyons II (Without Dying)
Beat Canyons II
Collect All The Coins (Canyons II)
Beat Canyons I (Without Dying)
Beat Canyons I
Collect All The Coins (Canyons I)
Run out of Lives
Lose 1 life
Throw 10 Water Balloons
Enter The Canyons